Question 425: Thermodynamics & KTG

Question

Two gases-argon (atomic radius 0.07 nm,
atomic weight 40) and xenon (atomic radius
0.1 nm, atomic weight 140) have the same
number density and are at the same
temperature. The raito of their respective mean
free times is closest to :

Accepted Answer

$$\lambda  = {1 \over {\sqrt 2 \pi {d^2}n}}$$
Mean free time, t = $${\lambda  \over v}$$
Also v $$ \propto $$ $$\sqrt {{T \over M}} $$
$$ 	herefore $$ t $$ \propto $$ $${{\sqrt M } \over d}$$
$${{{t_{Ar}}} \over {{t_{xe}}}}$$ = $${{d_{Xe}^2} \over {d_{Ar}^2}} 	imes \sqrt {{{{M_{Ar}}} \over {{M_{Xe}}}}} $$
= $${\left( {{{0.1} \over {0.07}}} ight)^2} 	imes \sqrt {{{40} \over {140}}} $$
= 1.09
$$ 	herefore $$ Nearest possible answer is 1.83.

Answer

2.3

Answer

1.83

Answer

4.67

Answer

3.67

Thermodynamics & KTG

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to :

Choose the correct answer: